Regularization

As with any inversion problem, the choice of regularization is important to impose constraints of the admissible models. For the multiple matching problem, since the character of both the primaries and the multiples is similar, it is best to use the same regularization for estimating the primary and multiple non-stationary filters. In an example like the ground-roll attenuation, where the character of the signal and the noise is so different, it may be better to use different regularization operator $A$ (or at least a different level of regularization $\epsilon$) for the estimate of the two filter banks. We used the same regularization for the noise and the signal in all of our examples.